Playing in his second game, and first start, back from a foot injury, Adreian Payne finished with a game-high 24 points and hit a 3 with 10 seconds left that tied the game at 58.
As has often happened during the junior's career, Jackson ended up with the ball in his hands late for a defining shot. Izzo knew it might be coming, so he put his best defender, Gary Harris, on Jackson.
Still no luck and the shot went through. A desperation 3 by Michigan State from midcourt banged off the rim as time expired, and the Wisconsin faithful erupted with applause. The victory snapped a three-game losing skid at home.
"Just (because) they lost a couple of home games -- and that's un-American in the Cheesehead State -- don't kid yourself. They're a very good team," Izzo said.
The Badgers (19-5, 6-5 Big Ten) committed 14 turnovers, six more than their NCAA-leading 8.3 per game, but gutted out a win over Michigan State (20-4, 9-2).
Nigel Hayes led Wisconsin with 14 points, while Sam Dekker added 11. Wisconsin shot 45 percent for the game, a threshold that means things are going wrong for the defensive Spartans. They've allowed opponents to shoot at least 44 percent in each four losses.
Travis Trice added 13 points for Michigan State, though Big Ten-leading scorer Gary Harris was held to six points on 3-of-20 shooting after being shadowed most of the afternoon by defensive specialist Josh Gasser.
And yet Michigan State still had a chance late, even with guard Keith Appling sitting out a second straight game with a wrist injury.
"I've got a feeling that Appling's out for a couple weeks. I have no idea. I can't answer the same questions, and I don't blame you for asking," Izzo said. "There's no break. There's no stress fracture. He can't even pass the ball; he can't move his hand."
Harris' long bucket with about 23 seconds left -- one of his few bright spots on the afternoon -- got the Spartans within three.
Wisconsin had a chance to turn it into a two-possession game, but Ben Brust missed the front end of a 1-and-1. Michigan State secured the rebound and called timeout.
Izzo drew up a play that ended up with Payne holding the ball. He had burned Wisconsin much of the night on the inside.
This time Payne hit from the outside and the Badgers faithful thought they were witnessing another late collapse at home. The loss to Ohio State more than a week ago ended up about the same way.
But Jackson, who has struggled much of the last month during Wisconsin's stretch of losing five of six, came up big. He finished with seven points and tied a career high with eight assists, but had five turnovers.
"That's sort of what they expected out of me is just to finish the game," Jackson said. "The pull-up was there, and I was blessed to be able to make it go in."
Wisconsin led by double-digits at one point in the second half. Things got shaky late.
After two empty Wisconsin possessions, the Spartans raced down in transition and Trice hit a 3 from the wing to get within 55-52 with 1:43 left.
They just couldn't break through in the end. A five-game winning streak over Wisconsin came to an end.
Gasser finished with 11 points and six rebounds for the Badgers. His straightaway 3 with 6:33 left gave the Badgers a huge lift and a six-point lead that was slowly chipped away by the Spartans.
But Gasser gave his team an ever bigger lift with his defense on the crafty Harris.
"Josh worked as hard as he normally works, and he got some help from teammates also," Wisconsin coach Bo Ryan said. "Josh did a great job of positioning, and chasing."